Method of feedforward turbocharger control for boosted engines with multi-route egr

ABSTRACT

An engine includes an exhaust gas recirculation system with a high pressure exhaust gas recirculation loop and a low pressure exhaust gas recirculation loop, and an air charging system. A method of controlling the air charging system includes monitoring an actual exhaust gas recirculation rate, operating conditions of a compressor and turbine in the air charging system. A compressor flow is determined based on a target exhaust gas recirculation rate, a target intake manifold pressure and the actual exhaust gas recirculation rate. A power requested by the compressor is determined based on the compressor flow, the target intake manifold pressure, and the monitored operating conditions of the compressor. A power to be generated by the turbine is determined based upon the power requested by the compressor. A turbine flow is determined based upon the power to be generated by the turbine and the monitored operating conditions of the turbine. A system control command is determined based on the turbine flow and the monitored operating conditions of the turbine. The air charging system is controlled based on the system control command.

TECHNICAL FIELD

This disclosure is related to control of internal combustion engines

BACKGROUND

The statements in this section merely provide background informationrelated to the present disclosure. Accordingly, such statements are notintended to constitute an admission of prior art.

Engine control includes control of parameters in the operation of anengine based upon a desired engine output, including an engine speed andan engine load, and resulting operation, for example, including engineemissions. Parameters controlled by engine control methods include airflow, fuel flow, and intake and exhaust valve settings.

Boost air can be provided to an engine to provide an increased flow ofair to the engine relative to a naturally aspirated intake system toincrease the output of the engine. A turbocharger utilizes pressure inan exhaust system of the engine to drive a compressor providing boostair to the engine. Exemplary turbochargers can include variable geometryturbochargers (VGT), enabling modulation of boost air provided for givenconditions in the exhaust system. A supercharger utilizes mechanicalpower from the engine, for example, as provided by an accessory belt, todrive a compressor providing boost air to the engine. Engine controlmethods control boost air in order to control the resulting combustionwithin the engine and the resulting output of the engine.

Exhaust gas recirculation (EGR) is another parameter that can becontrolled by engine controls. An exhaust gas flow within the exhaustsystem of an engine is depleted of oxygen and is essentially an inertgas. When introduced to or retained within a combustion chamber incombination with a combustion charge of fuel and air, the exhaust gasmoderates the combustion, reducing an output and an adiabatic flametemperature. EGR can also be controlled in combination with otherparameters in advanced combustion strategies, for example, includinghomogeneous charge compression ignition (HCCI) combustion. EGR can alsobe controlled to change properties of the resulting exhaust gas flow.Engine control methods control EGR in order to control the resultingcombustion within the engine and the resulting output of the engine. EGRsystem circuits can include multiple routes of providing exhaust gasinto the combustion chamber including high pressure (HP) exhaust gasrecirculation circuits and low pressure (LP) exhaust gas recirculationcircuits. In boosted engines, exhaust gas may be directed into theengine intake manifold via a high pressure route wherein the exhaust gasis directed back into the intake flow prior to flowing through the VGTsuch that the exhaust gas remains pressurized. The exhaust gas mayadditionally be directed back to the engine intake manifold through acircuit after passing through the VGT, at which point the exhaust gas isno longer under pressure.

Air handling systems for an engine manage the flow of intake air and EGRinto the engine. Air handling systems must be equipped to meet chargeair composition targets (e.g. an EGR fraction target) to achieveemissions targets, and meet total air available targets (e.g. the chargeflow mass flow) to achieve desired power and torque targets. Theactuators that most strongly affect EGR flow generally affect chargeflow, and the actuators that most strongly affect charge flow generallyaffect EGR flow. Therefore, an engine with a modern air handling systempresents a multiple input multiple output (MIMO) system with coupledinput-output response loops.

MIMO systems, where the inputs are coupled, i.e. the input-outputresponse loops affect each other, present well known challenges in theart. An engine air handling system presents further challenges. Theengine operates over a wide range of parameters including variableengine speeds, variable torque outputs, and variable fueling and timingschedules. In many cases, exact transfer functions for the system areunavailable and/or the computing power needed for a standard decouplingcalculation is not available. Multi-route EGR operation allows thesystem to run higher EGR rates at higher boost levels, but affects theVGT/compressor flow and power which impacts boost control design andperformance.

SUMMARY

An engine includes an exhaust gas recirculation system with a highpressure exhaust gas recirculation loop and a low pressure exhaust gasrecirculation loop, and an air charging system. A method of controllingthe air charging system includes monitoring an actual exhaust gasrecirculation rate, operating conditions of a compressor in the aircharging system and operating conditions of a turbine in the aircharging system. A compressor flow is determined based on a targetexhaust gas recirculation rate, a target intake manifold pressure andthe actual exhaust gas recirculation rate. A power requested by thecompressor in the air charging system is determined based on thecompressor flow, the target intake manifold pressure, and the monitoredoperating conditions of the compressor. A power to be generated by theturbine is determined based upon the power requested by the compressor.A turbine flow is determined based upon the power to be generated by theturbine and the monitored operating conditions of the turbine. A systemcontrol command for the air charging system is determined based on theturbine flow and the monitored operating conditions of the turbine. Theair charging system is controlled based on the system control command.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments will now be described, by way of example, withreference to the accompanying drawings, in which:

FIG. 1 schematically depicts an exemplary internal combustion engine,control module, and exhaust aftertreatment system, in accordance withthe present disclosure;

FIG. 2 schematically depicts an exemplary engine configuration includinga turbocharger, and a multi-route exhaust gas recirculation system, inaccordance with the present disclosure;

FIG. 3 schematically depicts an exemplary air charging multivariablecontrol system, using model-based feedforward control and feedbackcontrol methods, in accordance with the present disclosure;

FIG. 4 graphically depicts a comparison of compressor operating pointsrequired to achieve the same pressure-ratio across the compressor withhigh-pressure EGR flow and low-pressure EGR flow, in accordance with thepresent disclosure;

FIG. 5 schematically depicts an exemplary turbocharger feedforwardcontrol with high-pressure EGR flow and low-pressure EGR flow, inaccordance with the present disclosure;

FIG. 6 graphically depicts an exemplary EGR control scheme, including acomparison of a measured EGR rate and a desired EGR rate to an EGRactuator opening percentage, in accordance with the present disclosure;

FIG. 7 graphically depicts an exemplary boost control scheme, whereinboth high-pressure EGR and low-pressure EGR flows are considered,including a comparison of a measured intake manifold pressure and adesired intake manifold pressure to a VGT actuator opening percentage,in accordance with the present disclosure;

FIG. 8 graphically depicts exemplary data comparing actual VGT flow andestimated VGT flow, in accordance with the present disclosure;

FIG. 9 graphically depicts exemplary data comparing computed targetturbine inlet pressure and measured target turbine inlet pressure, inaccordance with the present disclosure; and

FIG. 10 depicts an exemplary process, in accordance with the presentdisclosure.

DETAILED DESCRIPTION

Referring now to the drawings, wherein the showings are for the purposeof illustrating certain exemplary embodiments only and not for thepurpose of limiting the same, FIG. 1 schematically depicts an exemplaryinternal combustion engine 10, control module 5, and exhaustaftertreatment system 65, in accordance with the present disclosure. Theexemplary engine includes a multi-cylinder, direct-injection,compression-ignition internal combustion engine having reciprocatingpistons 22 attached to a crankshaft 24 and movable in cylinders 20 whichdefine variable volume combustion chambers 34. The crankshaft 24 isoperably attached to a vehicle transmission and driveline to delivertractive torque thereto, in response to an operator torque request,TO_REQ. The engine preferably employs a four-stroke operation whereineach engine combustion cycle includes 720 degrees of angular rotation ofcrankshaft 24 divided into four 180-degree stages(intake-compression-expansion-exhaust), which are descriptive ofreciprocating movement of the piston 22 in the engine cylinder 20. Amulti-tooth target wheel 26 is attached to the crankshaft and rotatestherewith. The engine includes sensors to monitor engine operation, andactuators which control engine operation. The sensors and actuators aresignally or operatively connected to control module 5.

The engine is preferably a direct-injection, four-stroke, internalcombustion engine including a variable volume combustion chamber definedby the piston reciprocating within the cylinder between top-dead-centerand bottom-dead-center points and a cylinder head including an intakevalve and an exhaust valve. The piston reciprocates in repetitive cycleseach cycle including intake, compression, expansion, and exhauststrokes.

The engine preferably has an air/fuel operating regime that is primarilylean of stoichiometry. One having ordinary skill in the art understandsthat aspects of the disclosure are applicable to other engineconfigurations that operate either at stoichiometry or primarily lean ofstoichiometry, e.g., lean-burn spark-ignition engines or theconventional gasoline engines. During normal operation of thecompression-ignition engine, a combustion event occurs during eachengine cycle when a fuel charge is injected into the combustion chamberto form, with the intake air, the cylinder charge. The charge issubsequently combusted by action of compression thereof during thecompression stroke.

The engine is adapted to operate over a broad range of temperatures,cylinder charge (air, fuel, and EGR) and injection events. The methodsdisclosed herein are particularly suited to operation withdirect-injection compression-ignition engines operating lean ofstoichiometry to determine parameters which correlate to heat release ineach of the combustion chambers during ongoing operation. The methodsare further applicable to other engine configurations, includingspark-ignition engines, including those adapted to use homogeneouscharge compression ignition (HCCI) strategies. The methods areapplicable to systems utilizing multi-pulse fuel injection events percylinder per engine cycle, e.g., a system employing a pilot injectionfor fuel reforming, a main injection event for engine power, and whereapplicable, a post-combustion fuel injection event for aftertreatmentmanagement, each which affects cylinder pressure.

Sensors are installed on or near the engine to monitor physicalcharacteristics and generate signals which are correlatable to engineand ambient parameters. The sensors include a crankshaft rotationsensor, including a crank sensor 44 for monitoring crankshaft (i.e.engine) speed (RPM) through sensing edges on the teeth of themulti-tooth target wheel 26. The crank sensor is known, and may include,e.g., a Hall-effect sensor, an inductive sensor, or a magnetoresistivesensor. Signal output from the crank sensor 44 is input to the controlmodule 5. A combustion pressure sensor 30 is adapted to monitorin-cylinder pressure (COMB_PR). The combustion pressure sensor 30 ispreferably non-intrusive and includes a force transducer having anannular cross-section that is adapted to be installed into the cylinderhead at an opening for a glow-plug 28. The combustion pressure sensor 30is installed in conjunction with the glow-plug 28, with combustionpressure mechanically transmitted through the glow-plug to the pressuresensor 30. The output signal, COMB_PR, of the pressure sensor 30 isproportional to cylinder pressure. The pressure sensor 30 includes apiezoceramic or other device adaptable as such. Other sensors preferablyinclude a manifold pressure sensor for monitoring manifold pressure(MAP) and ambient barometric pressure (BARO), a mass air flow sensor formonitoring intake mass air flow (MAF) and intake air temperature (TIN),and a coolant sensor 35 monitoring engine coolant temperature (COOLANT).The system may include an exhaust gas sensor for monitoring states ofone or more exhaust gas parameters, e.g., temperature, air/fuel ratio,and constituents. One skilled in the art understands that there mayother sensors and methods for purposes of control and diagnostics. Theoperator input, in the form of the operator torque request, TO_REQ, istypically obtained through a throttle pedal and a brake pedal, amongother devices. The engine is preferably equipped with other sensors formonitoring operation and for purposes of system control. Each of thesensors is signally connected to the control module 5 to provide signalinformation which is transformed by the control module to informationrepresentative of the respective monitored parameter. It is understoodthat this configuration is illustrative, not restrictive, including thevarious sensors being replaceable with functionally equivalent devicesand routines.

The actuators are installed on the engine and controlled by the controlmodule 5 in response to operator inputs to achieve various performancegoals. Actuators include an electronically-controlled throttle valvewhich controls throttle opening in response to a control signal (ETC),and a plurality of fuel injectors 12 for directly injecting fuel intoeach of the combustion chambers in response to a control signal(INJ_PW), all of which are controlled in response to the operator torquerequest, TO_REQ. An exhaust gas recirculation valve 32 and coolercontrol flow of externally recirculated exhaust gas to the engineintake, in response to a control signal (EGR) from the control module. Aglow-plug 28 is installed in each of the combustion chambers and adaptedfor use with the combustion pressure sensor 30. Additionally, a chargingsystem can be employed in some embodiments supplying boost air accordingto a desired manifold air pressure.

Fuel injector 12 is a high-pressure fuel injector adapted to directlyinject a fuel charge into one of the combustion chambers in response tothe command signal, INJ_PW, from the control module. Each of the fuelinjectors 12 is supplied pressurized fuel from a fuel distributionsystem, and has operating characteristics including a minimum pulsewidthand an associated minimum controllable fuel flow rate, and a maximumfuel flow rate.

The engine may be equipped with a controllable valvetrain operative toadjust openings and closings of intake and exhaust valves of each of thecylinders, including any one or more of valve timing, phasing (i.e.,timing relative to crank angle and piston position), and magnitude oflift of valve openings. One exemplary system includes variable camphasing, which is applicable to compression-ignition engines,spark-ignition engines, and homogeneous-charge compression ignitionengines.

The control module 5 executes routines stored therein to control theaforementioned actuators to control engine operation, including throttleposition, fuel injection mass and timing, EGR valve position to controlflow of recirculated exhaust gases, glow-plug operation, and control ofintake and/or exhaust valve timing, phasing, and lift on systems soequipped. The control module is configured to receive input signals fromthe operator (e.g., a throttle pedal position and a brake pedalposition) to determine the operator torque request, TO_REQ, and from thesensors indicating the engine speed (RPM) and intake air temperature(Tin), and coolant temperature and other ambient conditions.

Control module, module, controller, control unit, processor and similarterms mean any suitable one or various combinations of one or more ofApplication Specific Integrated Circuit(s) (ASIC), electroniccircuit(s), central processing unit(s) (preferably microprocessor(s))and associated memory and storage (read only, programmable read only,random access, hard drive, etc.) executing one or more software orfirmware programs, combinational logic circuit(s), input/outputcircuit(s) and devices, appropriate signal conditioning and buffercircuitry, and other suitable components to provide the indicatedfunctionality. The control module has a set of control routines,including resident software program instructions and calibrations storedin memory and executed to provide the desired functions. The routinesare preferably executed during preset loop cycles. Routines areexecuted, such as by a central processing unit, and are operable tomonitor inputs from sensors and other networked control modules, andexecute control and diagnostic routines to control operation ofactuators. Loop cycles may be executed at regular intervals, for exampleeach 3.125, 6.25, 12.5, 25 and 100 milliseconds during ongoing engineand vehicle operation. Alternatively, routines may be executed inresponse to occurrence of an event.

FIG. 1 depicts an exemplary diesel engine, however, the presentdisclosure can be utilized on other engine configurations, for example,including gasoline-fueled engines, ethanol or E85 fueled engines, orother similar known designs. The disclosure is not intended to belimited to the particular exemplary embodiments disclosed herein.

FIG. 2 schematically depicts an exemplary engine configuration includinga turbocharger, and a multi-route exhaust gas recirculation system, inaccordance with the present disclosure. The exemplary engine ismulti-cylinder and includes a variety of fueling types and combustionstrategies known in the art. Engine system components include an intakeair filter 150, a throttle valve for low-pressure EGR 132, an intake aircompressor including a turbine 46 and an air compressor 45, a charge aircooler 152, an intake air throttle valve 136, a high-pressure EGR valve140 and cooler 154, an intake manifold 50, exhaust manifold 60, a dieseloxidation catalyst (DOC) and diesel particulate filter (DPF) 156, athrottle valve for low-pressure EGR 144, a low-pressure EGR cooler 158,and a low-pressure EGR valve 148. Ambient intake air is drawn intocompressor 45 through intake 171. Pressurized intake air and EGR floware delivered to intake manifold 50 for use in engine 10. Exhaust gasflow exits engine 10 through exhaust manifold 60, drives turbine 46, andexits through exhaust tube 170. The depicted EGR system includes a highpressure EGR system, delivering pressurized exhaust gas from exhaustmanifold 60 to intake manifold 50. The depicted EGR system additionallyincludes, a low pressure EGR system, delivering low pressure exhaust gasfrom exhaust tube 170 to intake 171. Sensors are installed on the engineto monitor physical characteristics and generate signals which arecorrelatable to engine and ambient parameters. The sensors preferablyinclude an ambient air pressure sensor 112, an ambient or intake airtemperature sensor 114, and a mass air flow sensor 116 (all which can beconfigured individually or as a single integrated device), an intakemanifold air temperature sensor 118, an MAP sensor 120, an exhaust gastemperature sensor 122, an air throttle valve position sensor 134 and ahigh-pressure EGR valve position sensor 138, a turbine vane positionsensor 124, as well as low-pressure EGR throttle valve position sensors130 and 142, and a low-pressure EGR valve position sensor 146. Enginespeed sensor 44 monitors rotational speed of the engine. Each of thesensors is signally connected to the control module 5 to provide signalinformation which is transformed by the control module 5 to informationrepresentative of the respective monitored parameter. It is understoodthat this configuration is illustrative, not restrictive, including thevarious sensors being replaceable within functionally equivalent devicesand routines and still fall within the scope of the disclosure.Furthermore, the intake air compressor may include alternativeturbocharger configurations within the scope of this disclosure.

The intake air compressor includes a turbocharger including an aircompressor 45 positioned in the air intake of the engine which is drivenby turbine 46 that is positioned in the exhaust gas flowstream. Turbine46 can include a number of embodiments, including a device with fixedvane orientations or variable vane orientations. Further, a turbochargercan be used as a single device, or multiple turbochargers can be used tosupply boost air to the same engine.

Variable geometry turbochargers (VGT) enable control of how muchcompression is performed on intake air. A control signal can modulateoperation of the VGT, for example, by modulating an angle of the vanesin the compressor and/or turbine. Such exemplary modulation can decreasethe angle of such vanes, decreasing compression of the intake air, orincrease the angle of such vanes, increasing compression of the intakeair. VGT systems allow a control module to select a level of boostpressure delivered to the engine. Other methods of controlling avariable charger output, for example, including a waste gate or a bypassvalve, can be implemented similarly to a VGT system, and the disclosureis not intended to be limited to the particular exemplary embodimentsdisclosed herein for controlling boost pressure delivered to the engine.

Exemplary diesel engines are equipped with common rail fuel-injectionsystems, EGR systems, and VGT systems. Exhaust gas recirculation is usedto controllably decrease combustion flaming temperature and reduce NOxemissions. VGT systems are utilized to modulate boost pressures tocontrol a manifold air pressure and increase engine output. Toaccomplish engine control including control of the EGR and VGT systems,a multi-input multi-output air charging control module (MIMO module) canbe utilized. A MIMO module enables computationally efficient andcoordinated control of EGR and VGT based upon a single set of inputsdescribing desired engine operation. Such input, for example, caninclude an operating point for the engine describing an engine speed andan engine load. It will be appreciated that other parameters can beutilized as input, for example, including pressure measurementsindicating an engine load.

Coupled MIMO control of both EGR and VGT, or control fixing response ofboth EGR and VGT based upon any given input, is computationallyefficient and can enable complex control responses to changing inputsthat might not be computationally possible in real-time based uponindependent control of EGR and VGT. However, coupled control of EGR andVGT, including fixed responses of both parameters for any given input,requires simplified or best fit calibrations of the coupled controls inorder to control both fixed responses. As a result, such calibrationscan be challenging and can include less than optimal engine performancebased upon the simplified control calibrations selected. EGR and VGT,for example, might optimally react differently to a rate of change inload or to engine temperatures. Additionally, control of EGR or VGT canreach limit conditions and result in actuator saturation. Coupledcontrol resulting in actuator saturation can cause a condition known inthe art as wind-up wherein expected behavior of the system and desiredcontrol of the system diverge and result in control errors even afterthe actuator saturation has been resolved. Additionally, control of EGRand VGT by a MIMO module is nonlinear, and defining the coupledfunctional relationships to provide the desired control outputs requiresextensive calibration work.

VGT commands are one way to control boost pressure. However, othercommands controlling a boost pressure such as a boost pressure commandor a manifold air pressure command can be utilized similarly in place ofVGT commands.

The engine configuration, such as the exemplary engine configuration,including a turbocharger, as is schematically depicted in FIG. 2 may berepresented by a mathematical model. Model-based nonlinear control maybe applied to transform desired air and charging targets to individualflow or power for each actuator, such as exhaust gas recirculation flow,intake air flow, and turbine power. An actuator position for each of theEGR valve, air throttle valve, and the VGT control can be uniquelydetermined based on the individual flow or power values, additionallyresulting in a decoupled and nearly linearized system for feedbackcontrol. A method to control an engine including EGR, air throttle andair charging control includes utilizing physics model-based feedforwardcontrol, or feedback linearization control to decouple the controls of amultivariable system.

With a boosted engine configuration that includes multi-route EGR loopsthe system may operate running higher EGR rates at higher boost levels,however this affects the turbine and compressor flow and power whichimpacts boost control design and performance. By utilizing a physicalmodel-based air charging control routine, the model-based controls canmodulate air charging actuators to minimize the impact of varyinghigh-pressure/low-pressure EGR rates on the boosting system. Based on aturbocharger energy balance model the desired boost may be maintained byadapting the VGT position to different combinations of HP and LP EGR fora given desired overall in-cylinder EGR rate. Unlike boost controlmethods that utilize look-up tables as feedforward control withouttaking into account the EGR operation and calibration, model basedcontrols eliminate boost control recalibration against any changes ofthe mix between high-pressure and low-pressure EGR loops. This reducescouplings/interactions between the boost system and the multiple EGRloops. Model-based feedforward boost control additionally enhancesrobustness against system variations and environmental changes such asambient temperature and pressure, reduces feedback control calibration,and improves transient responses via model-based feedforward control.

In accordance with the exemplary engine configuration depicted in FIG.2, the various LP, HP, and combined EGR rates of the system air and EGRflows may be expressed by a series of relationships. The long-route EGRmixing point is the point where the LP EGR flow W_(egr,LP) passesthrough LP EGR valve 148 and mixes with the fresh air flow W_(air) as itpasses through the LP EGR throttle valve 132. Low pressure EGR rater_(LP) at the long-route EGR mixing point may be expressed by thefollowing relationship.

$\begin{matrix}{r_{LP} = \frac{W_{{egr},{LP}}}{W_{air} + W_{{egr},{LP}}}} & \lbrack 1\rbrack\end{matrix}$

The short-route EGR mixing point is the point where the HP EGR flowW_(egr,HP) passes through HP EGR valve 140 and mixes with the compressorflow W_(c) as it passes through the intake throttle valve 136. Highpressure EGR rate r_(LP) at the short-route EGR mixing point may beexpressed by the following relationship.

$\begin{matrix}{r_{HP} = \frac{W_{{egr},{HP}}}{W_{c} + W_{{egr},{HP}}}} & \lbrack 2\rbrack\end{matrix}$

The in-cylinder EGR rate r in the cylinder charge flow W_(cyl) may beexpressed by the following relationships.

$\begin{matrix}{r = \frac{W_{{egr},{HP}} + W_{{egr},{LP}}}{W_{cyl}}} & \lbrack 3\rbrack \\{r = {r_{HP} + {\left( {1 - r_{HP}} \right)*r_{LP}}}} & \lbrack 4\rbrack\end{matrix}$

The split EGR ratio may then be expressed by the following relationship.

$\begin{matrix}{r_{SP} = {\frac{W_{{egr},{LP}}}{W_{{egr},{LP}} + W_{{egr},{HP}}} = {1 - \frac{r_{HP}}{r}}}} & \lbrack 5\rbrack\end{matrix}$

When the system is operating at steady-state, the system flows,including the cylinder charge flow W_(cyl), the flow out of the turbine46 W_(t), and the flow into the compressor W_(c), may be expressed bythe following relationships:

$\begin{matrix}{W_{cyl} = {\eta_{v}\frac{V_{d}}{120\; R*T_{i}}P_{i}*N}} & \lbrack 6\rbrack\end{matrix}$

wherein N is engine speed,

-   -   V_(d) is engine displacement volume,    -   P_(i) is the intake pressure,    -   R is the universal gas constant,    -   η_(v) is the engine volumetric efficiency, and    -   T_(i) is the intake temperature;

W _(t)=(1−r _(HP))*W _(cyt) +W _(f)  [7]

W _(c)=(r _(HP))*W _(cyt)[8]

Flow into the compressor W_(c) may alternatively be expressed by thefollowing relationship.

$W_{c} = \frac{W_{air}}{\left( {1 - r_{LP}} \right)}$

At steady state the burned gas fractions at varying points in the systemmay also be expressed in relation to EGR rates. The burned gas fractionat the exhaust F_(x), the burned gas fraction at the low pressure EGRmix point F_(LP,mix), and the burned gas fraction at the intake F_(i)may be represented by the following relationships in a dynamic state.

F _(egr,HP)(t)=F _(x)(t−τ _(HP))  [9]

m _(i) {dot over (F)} _(i) =W _(egr,HP)*(F _(x)(t−τ _(Hp))−F _(i))+W_(itv)*(F _(itv) −F _(i))  [10]

F _(egr,LP)(t)=F _(x)(t−τ _(LP))  [11]

m _(LP,mix) {dot over (F)} _(LP,mix) =W _(egr,LP)*(F _(x)(t−τ _(LP))−F_(LP,mix))−W _(air) F _(LP,mix)  [12]

If the system is in steady-state, these relationships may alternativelybe expressed by the following relationships.

$\begin{matrix}{F_{{egr},{HP}} = F_{x}} & \lbrack 13\rbrack \\{F_{{egr},{LP}} = F_{x}} & \lbrack 14\rbrack \\{F_{x} = \frac{1 + {AFR}_{s}}{1 + {AFR}}} & \lbrack 15\rbrack \\{F_{{LP},{mix}} = {r_{LP}*F_{x}}} & \lbrack 16\rbrack \\{F_{i} = {{r_{HP}*F_{x}} + {\left( {1 - r_{HP}} \right)*F_{{LP},{mix}}}}} & \lbrack 17\rbrack \\{F_{i} = {{r_{HP}*F_{x}} + {\left( {1 - r_{HP}} \right)*r_{LP}*F_{x}}}} & \lbrack 18\rbrack\end{matrix}$

The burned fraction at a particular point is generally related to oxygenconcentrations, and the relationship between a burned fraction and anoxygen concentration at a particular point may be expressed by thefollowing relationship.

O ₂≅0.23*(1−F)  [19]

An exemplary system model for the model based nonlinear control can beexpressed as nonlinear differential equation in accordance with thefollowing relationship.

{dot over (y)}=F(y)+Bu  [20]

The MIMO feedforward control applied to the inputs u in the exemplarysystem model expressed above can be expressed by the followingrelationship.

u=−B ⁻¹ F(y)+B ⁻¹ v  [21]

The term −B⁻¹F(y) expresses the feedback linearization of the system ify is an actual measured or estimated parameter from the system, or itexpresses the feedforward control of the system if y is replaced by itsdesired reference command to track. The feedback controller v canutilize proportional-integral-derivative (PID), linear quadraticregulator (LQR), or model predictive control (MPC) feedback controlmethods with minimum gains scheduling required. The multivariable systemoutput vector {dot over (y)} can be decoupled into a linear SISOfeedback system, as is expressed by the following relationship.

$\begin{matrix}{\overset{.}{y} = {\begin{bmatrix}{\overset{.}{y}}_{1} \\{\overset{.}{y}}_{2} \\\vdots \\{\overset{.}{y}}_{n}\end{bmatrix} = {\begin{bmatrix}v_{1} \\v_{2} \\\vdots \\v_{n}\end{bmatrix} = v}}} & \lbrack 22\rbrack\end{matrix}$

The input vector u is input into the system model which appliesmodel-based multivariable feedforward control to replace lookup tables,and additionally applies feedback control to improve tracking againstunmodeled uncertainties. The output vector {dot over (y)} is thendecoupled into linear SISO feedback vector v.

An exemplary physics based air and charging system model of theexemplary engine configuration, including a turbocharger as isschematically depicted in FIG. 2 is expressed, in accordance with thebasic system model relationships expressed above, by the following setof relationships.

$\begin{matrix}{\mspace{79mu} {{\overset{.}{p}}_{rc} = {{- {{cP}_{c}\left( {p_{rc},\frac{W_{c}\sqrt{T_{uc}}}{p_{uc}}} \right)}} + {J\left( {{\overset{.}{W}}_{c},W_{c}} \right)} + {cP}_{t}}}} & \lbrack 23\rbrack \\{\begin{bmatrix}{\frac{V_{i}}{{RT}_{i}}{\overset{.}{P}}_{i}} \\{m_{i}{\overset{.}{F}}_{i}} \\{m_{c}{\overset{.}{F}}_{c}}\end{bmatrix} = {\begin{bmatrix}{- W_{cyl}} \\0 \\0\end{bmatrix} + {\begin{bmatrix}1 & 1 & 0 \\{F_{c} - F_{i}} & {F_{x} - F_{i}} & 0 \\{- F_{c}} & 0 & {F_{x}\left( {t - \tau} \right)}\end{bmatrix}\begin{bmatrix}W_{itv} \\W_{{egr},{HP}} \\W_{{egr},{LP}}\end{bmatrix}}}} & \lbrack 24\rbrack\end{matrix}$

wherein p_(rc) is the compressor pressure ratio,

-   -   P_(c) is compressor power,    -   P_(t) is turbine power,    -   W_(c) is compressor flow,    -   T_(uc) is temperature upstream of the compressor,    -   p_(uc) is pressure upstream of the compressor,    -   V_(i) is the intake volume,    -   R is the universal gas constant,    -   T_(i) is the intake temperature,    -   P_(i) is the intake pressure,    -   m_(i) is the intake mass,    -   m_(c) is the air mass before the compressor (at the low pressure        EGR mix point),    -   F_(i) is the burned gas fraction at the intake,    -   F_(c) is the burned gas fraction before the compressor (at the        low pressure EGR fix point),    -   F_(x) is the burned gas fraction at the exhaust,    -   t is time, and    -   τ is a time delay.        The burned gas fraction before the compressor, F_(c), may be        expressed by the following relationship.

F _(c) =r _(LP) *F _(x)  [25]

The power balance expressed in relationship [23] is merely an exemplarypower balance expression, and may alternatively be expressed by any ofthe following relationships.

$\begin{matrix}{{\tau*{\overset{.}{P}}_{c}} = {{- P_{c}} + {\eta_{m}*P_{t}}}} & \lbrack 26\rbrack \\{{\frac{1}{2}J_{t}\frac{\left( N_{t}^{2} \right)}{t}} = {P_{t} - P_{c} - P_{tf}}} & \lbrack 27\rbrack \\{{\frac{1}{2}J_{t}\frac{\left( N_{t}^{2} \right)}{t}} = {{\eta_{m}P_{t}} - P_{c}}} & \lbrack 28\rbrack\end{matrix}$

wherein N_(t) is the turbocharger shaft speed,

-   -   J is the turbocharger shaft inertia,    -   η_(m) is the mechanical efficiency at the turbocharger shaft,        and    -   P_(tf) is the friction at the turbocharger shaft.

Flow through an EGR system can be modeled to estimate the flow basedupon a number of known inputs. Flow through the EGR system can bemodeled as flow through an orifice, wherein the orifice primarilyincludes an EGR valve or an orifice or venturi to a particular design.According to one exemplary embodiment, EGR flow, W_(egr), can be modeledaccording to the following orifice flow relationship.

$\begin{matrix}{W_{egr} = {A_{egr}\frac{P_{x}}{\sqrt{{RT}_{egr}}}{\Psi ({PR})}}} & \lbrack 29\rbrack\end{matrix}$

PR is a pressure ratio or ratio of intake pressure or pressure ofcharged air in the intake system at the outlet of the EGR system, P_(i),to exhaust pressure or pressure in the exhaust system at the inlet ofthe EGR system upstream of the charging system, P_(x). T_(egr) canindicate a temperature of the exhaust gas or exhaust gas temperature atthe inlet of the EGR system. According to one exemplary embodiment,T_(egr) can be measured as an exit temperature of the EGR cooler.A_(egr) is the effective flow area of the EGR system. R is the universalgas constant, known in the art. A critical pressure ratio, PR_(c), canbe expressed by the following relationship.

$\begin{matrix}{{PR}_{c} = \left( \frac{2}{\gamma + 1} \right)^{\frac{\gamma}{\gamma - 1}}} & \lbrack 30\rbrack\end{matrix}$

γ is a specific heat ratio, known in the art. If PR is greater thanPR_(c), then flow is subsonic. If PR is less than or equal to PR_(c),then flow is choked. Ψ(PR) is a non-linear function and can be expressedby the following relationship.

$\begin{matrix}{{\Psi ({PR})} = \left\{ \begin{matrix}\sqrt{\frac{2\gamma}{\gamma - 1}\left( {{PR}^{2/\gamma} - {PR}^{{({\gamma + 1})}/\gamma}} \right)} & {{PR}_{c} < {PR} < {1\mspace{14mu} ({subsonic})}} \\{\gamma^{1/2}\left( \frac{2}{\gamma + 1} \right)}^{\frac{\gamma + 1}{2{({\gamma - 1})}}} & {{PR} \leq {{PR}_{c}\mspace{11mu} ({choked})}}\end{matrix} \right.} & \lbrack 31\rbrack\end{matrix}$

A_(egr) can be expressed as a function of EGR valve position, x_(egr).However, based upon detailed modeling and experimental data, including adetermination of heat loss through the walls of the system, a moreaccurate estimation for A_(egr) can be expressed as a function ofx_(egr) and PR, which can be expressed by the following relationship.

A _(egr) =A _(egr)(x _(egr) ,PR)  [32]

The method disclosed above assumes that the EGR system includes anoutlet downstream of the charging system compressor and an inletupstream of the charging system turbo unit or turbine. It will beappreciated that a different embodiment can be utilized with an EGRsystem including an outlet upstream of the charging system compressorand an inlet downstream of the charging system turbo unit or turbine orin the exhaust system of a vehicle utilizing a supercharger without aturbine. It will be appreciated that the above relationships and theassociated inverse flow model can be modified for use with a number ofexemplary EGR and charging system configurations, and the disclosure isnot intended to be limited to the particular exemplary embodimentsdisclosed herein.

FIG. 3 schematically depicts an exemplary air charging multivariablecontrol system, using model-based feedforward control and feedbackcontrol methods, in accordance with the present disclosure. Air chargingsystem 311 receives commands and produces outputs. A number of modulesand control strategies are depicted developing the commands, includingthe state variable observer module 314, the linear control strategy 313including feedback control module 302, and the nonlinear controlstrategy 312. Desired operating parameter points or target operatingpoints may include desired compressor pressure ratio p_(rc) _(_) _(des)320, desired intake manifold pressure p_(i) _(_) _(des) 321, estimatedburned gas fraction at the intake F_(i) 322, and estimated burned gasfraction before the compressor, at the low pressure EGR fix point, F_(c)323. These desired/target points may alternatively be expressed in termsof EGR rates or oxygen concentrations at the desired mix point, as isdescribed by the relationships described herein. The target points may,as exemplary, include any pair of the variables r_(HP), r_(LP), r_(S),F_(i), F_(c), O_(2,i), and O_(2,c) as are described herein. Thesedesired operating parameter points are compared with respective feedbacksignals 348, 349, 350 and 351 which are determined by either directsensor measurements or the state variable observer module 314 based onthe actual operating parameters of the air charging system 311. Theseoperating parameters are represented by operating parameter signals 344,345, 346 and 347, and may include, as exemplary, intake manifoldpressure, intake manifold temperature, air mass, ambient pressure, andambient temperature. The air charging system parameters may be monitoredby sensors or alternatively estimated by the state variable observermodule 314 if no sensor is present. The monitored and estimated systemoperating parameters may be used to determine feedback signals. Thefeedback signals describe actual compressor pressure ratio p_(rc) 348,actual intake manifold pressure p_(i) 349, actual burned gas fraction atthe intake F_(i) 350, and actual burned gas fraction before thecompressor, measured at the low pressure EGR fix point F_(c) 351. Thecomparison of the desired operating parameters and the respective actualoperating parameters determines error terms for each parameter includinga compressor pressure ratio error term 324, an intake manifold pressureerror term 325, a burned gas fraction at the intake error term 326, anda burned gas fraction before the compressor error term 327. These errorterms are then input into the feedback control module 302 of the linearcontrol strategy 313. The feedback control method implemented by thefeedback control module 302 determines feedback control signals v₁ 328,v₂ 329, v₃ 330 and v₄ 331. Desired operating parameter points, includingdesired compressor pressure ratio p_(rc) _(_) _(des) 320, desired intakemanifold pressure p_(i) _(_) _(des) 321, estimated burned gas fractionat the intake F_(i) 322, and estimated burned gas fraction before thecompressor F_(c) 323 are additionally input into feedforward controlmodule 301, and feedforward signals including compressor pressure ratiofeedforward signal 332, intake manifold pressure feedforward signal 333,burned gas fraction at the intake feedforward signal 334, and burned gasfraction before the compressor feedforward signal are output. Feedbackcontrol signals 328, 329, 330 and 331, as well as feedforward signals332, 333, 334 and 335 are input into nonlinear control strategy 312.These signals are utilized in calculating turbine power transfer rateR_(t) 336, air flow W_(itv) 337, HP EGR flow W_(egrHP) 338, and LP EGRflow W_(egrLP) 339 at points 303, 304, 305 and 306. The calculations todetermine these feedforward signals can be expressed by the followingrelationships:

$\begin{matrix}{R_{t} = {\frac{1}{h_{t}}\left( {P_{c} + \frac{v_{1}}{c}} \right)}} & \lbrack 33\rbrack\end{matrix}$

wherein P_(c) is the compressor power, and

-   -   h_(t) is the exhaust energy flow;

$\begin{matrix}{\begin{bmatrix}W_{itv} \\W_{{egr},{HP}}\end{bmatrix} = {\begin{bmatrix}\frac{F_{x} - F_{i}}{F_{x} - F_{c}} & {- \frac{1}{F_{x} - F_{c}}} \\\frac{F_{i} - F_{c}}{F_{x} - F_{c}} & \frac{1}{F_{x} - F_{c}}\end{bmatrix}\begin{bmatrix}{W_{cyl} + v_{2}} \\v_{3}\end{bmatrix}}} & \lbrack 34\rbrack \\{W_{{egr},{LP}} = {{r_{LP}W_{itv}} + {\frac{1}{F_{x}}v_{4}}}} & \lbrack 35\rbrack\end{matrix}$

Through the matrix multiplication of relationship [34], feedforwardmodule 301, feedback control module 302 and nonlinear control strategy312 also have access to information about the engine operation, andoperating parameters of the air charging system 311, such as operatingparameter signals 344, 345, 346 and 347 which may either be monitored bysensors or alternatively estimated by the state variable observer module314. Signal 336, which may be either turbine power transfer rate R_(t),or turbine power P_(t) as the two are related by P_(t)=h_(t)*R_(t), airflow W_(itv) 337, HP EGR flow W_(egrHP) 338, and LP EGR flow W_(egrLP)339 are then transformed into system control commands including a VGTcommand u_(vgt) 340, an air throttle valve command u_(itv) 341, a HP EGRvalve command u_(egr) 342, and a LP EGR valve command 343. The VGTcommand u_(vgt) 340, air throttle valve command u_(itv) 341, HP EGRvalve command u_(egr) 342, and LP EGR valve command 343 are then used tocontrol the air charging system 311. The transformation of the turbinepower transfer rate 336, air flow 337, HP EGR flow 338, and LP EGR flow339 into the system control commands can be achieved through the use ofan inverse flow model or an inverse of a physical model of a system.

An inverse flow model or an inverse of a physical model of a system canbe useful in determining settings required to achieve a desired flowthrough an orifice in the system. Flow through a system can be modeledas a function of a pressure difference across the system and a flowrestriction in the system. Known or determinable terms can besubstituted and the functional relationship manipulated to make aninverse flow model of the system useful to determine a desired systemsetting to achieve a desired flow. Exemplary methods disclosed hereinutilize a first input of an effective flow area or of a flow restrictionfor the system being modeled, and a second input including a pressurevalue for the system of pressure moving the flow through the system. Oneexemplary method of decoupled feed forward control of an EGR valve caninclude utilizing an inverse flow model of the system embodied in amixed polynomial based upon the inverse model and calibrated terms.Another exemplary method of decoupled feed forward control of an EGRvalve can include utilizing a dimensional table-based approach. Anotherexemplary method of decoupled feed forward control of an EGR valve caninclude utilizing an exponential polyfit model. An exemplary method ofdecoupled feed forward control of air throttle can utilize an inverse ofthe physical model of the system, a dimensional table approach, or anexponential polyfit model. An exemplary method of decoupled feed forwardcontrol of a charging system, such as a turbocharger equipped with aVGT, can utilize an inverse of the physical model of the system, adimensional table approach, or an exponential polyfit model.

These methods can be utilized individually or in combination, anddifferent methods can be utilized for the same system for differentconditions and operating ranges. A control method can utilize an inverseflow model to determine a feed forward control command for a firstselection including one of the EGR circuit, the air throttle system, andthe charging system. The control method can additionally utilize asecond inverse flow model to determine a second feed forward controlcommand for a second selection including another of the EGR circuit, theair throttle system, and the charging system. The control method canadditionally utilize a third inverse flow model to determine a thirdfeed forward control command for a third selection including another ofthe EGR circuit, the air throttle system, and the charging system. Inthis way, a control method can control any or all of the EGR circuit,the air throttle system, and the charging system.

A method to control EGR flow by an inverse control method according toan inverse model of EGR flow is disclosed in co-pending and commonlyassigned application Ser. No. 12/982,994, corresponding to publicationUS 2012-0173118 A1, which is incorporated herein by reference.

As indicated related to FIG. 3, feedback control module 302 of linearcontrol strategy 313 determines feedback control signals 328, 329, 330and 331 using feedback control methods. The exemplary feedback controlmethods used by the feedback control module of FIG. 3 can include PIDcontrol. In an exemplary embodiment, the PID control module can bedesigned as multiple individual modules, each assigned to a particulardesired operating parameter input in order to output decoupled feedbackcontrol signals. The feedback control module may alternatively utilizemodel predictive control or linear quadratic regulator control methods.

FIG. 4 graphically depicts a comparison of compressor operating pointsrequired to achieve the same pressure-ratio across the compressor withhigh-pressure EGR flow and low-pressure EGR flow, in accordance with thepresent disclosure. This comparison illustrates a turbocharger operatingpoint shift for varying HP EGR and LP EGR ratios. The x-axis 401represents compressor flow W_(c), the y-axis 402 represents the pressureratio across the compressor p_(rc). Horizontal line 412 represents aconsistent pressure-ratio across the compressor, specifically, thepressure at the compressor outlet, P_(t). Vertical line 410 representsthe compressor flow necessary to achieve pressure-ratio 412 across thecompressor with only HP EGR, as is represented by point 420. Verticalline 411 represents the compressor flow necessary to achievepressure-ratio 412 across the compressor with only LP EGR, as isrepresented by point 421.

An overall in-cylinder EGR rate, r, could be achieved with differentcombinations of LP HGR and HP EGR. Overall in-cylinder EGR rate r can beexpressed by the following relationship.

r=r _(HP)+(1−r _(HP))*r _(LP)  [36]

If only LP EGR is being utilized, compressor flow W_(c) is equal to theflow into the cylinders at steady state W_(cyt). If only HP EGR is beingutilized, then compressor flow W_(c) is reduced by the HP EGR flow andcan be expressed by the following relationship.

W _(c)=(1−r _(HP))*W _(cyt)  [37]

Point 420 shows that to achieve a desired pressure-ratio across thecompressor with only HP EGR being utilized, the compressor flow 410 maybe expressed by the following relationship.

(1−r)*k*P _(i)  [38]

Point 421 shows that to achieve a desired pressure-ratio across thecompressor with only LP EGR being utilized, the compressor flow 411 maybe expressed by the following relationship.

k*P _(i)  [39]

In both of these relationships, k is a calculated term representingcylinder charge flow W_(cyt) as is expressed in relationship [6] and maybe expressed by the following relationship.

$\begin{matrix}{k = {\eta_{v}\frac{V_{d}}{120R*T_{i}}N}} & \lbrack 40\rbrack\end{matrix}$

The turbocharger power shift is utilized due to how overall EGR isachieved to adapt the feedforward VGT command for a given desired boostpressure and LP/HP EGR rate. The turbocharger power shift may beexpressed by the following relationship:

$\begin{matrix}{P_{c} = {W_{c}T_{a}{{c_{p}\left\lbrack {\left( \frac{p_{i}}{p_{a}} \right)^{\mu} - 1} \right\rbrack}/\eta_{c}}}} & \lbrack 41\rbrack\end{matrix}$

wherein μ is the specific heat ratio,

-   -   c_(p) is specific heat under constant pressure, and    -   η_(c) is compressor efficiency.

FIG. 5 schematically depicts an exemplary turbocharger feedforwardcontrol 500 with both high-pressure EGR flow and low-pressure EGR flow,in accordance with the present disclosure. Reference EGR rate r 510, andreference boost pressure p_(i) 511 are input into compressor flow module501 which determines compressor flow W_(c) 512 based on target boostp_(i) 511 and target/actual EGR rate r 510. The HP EGR rate r_(HP) maybe determined based on the relationship between in-cylinder EGR rate r,r_(HP) and r_(LP) expressed in relationship [28]. With both LP EGR andHP EGR operating, r_(HP) and r_(LP) may be used as targets overoperating maps, or computed from measured or estimated burned gasfractions at mixing points (F_(i), F_(LP,mix)) and burned exhaust gasfraction F_(x). These values may come from sensors, or from a stateobserver estimator, and may be expressed by the following relationships.

$\begin{matrix}{r_{HP} = \frac{r - r_{LP}}{1 - r_{LP}}} & \lbrack 42\rbrack \\{r = {F_{i}/F_{x}}} & \lbrack 43\rbrack \\{r_{LP} = {F_{{LP},{mix}}/F_{x}}} & \lbrack 44\rbrack\end{matrix}$

Compressor flow 512 may be determined by the following relationship.

W _(c)=(1−r _(HP))*k*p _(i)  [45]

Compressor flow 512 and reference boost pressure 511 are input intocompressor power/flow relation module 502 which determines compressorpower P_(c) 514 based on compressor flow 512, reference boost pressure511 and additional system inputs 513, which may include temperatureupstream of the compressor T_(uc), and pressure upstream of thecompressor p_(uc), which is determined based upon air flow W_(air), lowpressure throttle valve control u_(ptv), ambient pressure p_(a), andambient temperature T_(a). These compressor inlet conditions may beexpressed by the following relationships based on the orificerelationship:

$\begin{matrix}{{\Psi \left( {p_{uc}/p_{a}} \right)} = {W_{air}*{\frac{\sqrt{{RT}_{a}}}{p_{a}}/{A_{lptv}\left( u_{iptv} \right)}}}} & \lbrack 46\rbrack\end{matrix}$

wherein A_(lptv) is the effective area of the low pressure throttlevalve, and

-   -   u_(lptv) is the low pressure throttle valve control.

T _(uc) =r _(LP) *T _(egr,LP)+(1−r _(LP))*T _(a)[47]

Wherein T_(egr,LP) is the temperature of the low pressure EGR, andCompressor power/flow relation module 502 determines compressor power514 based on the relationship expressed by relationship [33] herein.Compressor power 514 is then input into the turbocharger power transfermodule 503 which determines turbine power P_(T) 515 based on thecompressor power. The relationship between turbine flow and turbinepower may be expressed by the following relationship:

$\begin{matrix}{P_{t} = {c_{p}T_{x}W_{t}{\eta_{t}\left\lbrack {1 - \left\lbrack \frac{p_{s}}{p_{x}} \right\rbrack^{\mu}} \right\rbrack}}} & \lbrack 48\rbrack\end{matrix}$

wherein ∂2 _(t) is the turbine efficiency,

-   -   T_(x) is exhaust temperature,    -   p_(s) is pressure at the downstream of turbine (turbine outlet        pressure), and    -   p_(x) is exhaust pressure.        The turbocharger power transfer dynamics may be represented by        the following relationships:

τ*{dot over (P)} _(c) =−P _(c) +n _(m) *P _(t)  [49]

(τ*s+1)P _(c)=η_(m)  [50]

wherein s is the differential operator from differentiation in Laplacedomain. Based on the turbine flow-power relationship, the compressorflow-power relationship and the turbocharger power transfer dynamics,the turbocharger power balance may be expressed by the followingrelationship:

$\begin{matrix}{{\frac{T_{uc}}{T_{x}}*\frac{\left( {{\tau s} + 1} \right)}{\eta_{m}\eta_{t}\eta_{c}}*\frac{\left\lbrack \frac{p_{i}}{p_{uc}} \right\rbrack^{\mu} - 1}{1 - \left\lbrack \frac{p_{s}}{p_{x}} \right\rbrack^{\mu}}} = {\frac{W_{t}}{W_{c}} \cong \frac{W_{c}^{d} + W_{f}^{d}}{W_{c}}}} & \lbrack 51\rbrack\end{matrix}$

wherein delayed MAF flow W^(d) _(c), and delayed fuel flow W^(d) _(f)are used to replace the current turbine flow.

Turbine power 515 is input into turbine power/flow relation module 504,as are additional system inputs 516 which may include pressure at theturbine input p_(t,in), temperature at the turbine input T_(t,in) andpressure at the turbine output p_(t,out). Turbine power/flow relationmodule 504 outputs a turbine flow W_(t) 517 based on these inputs.Turbine flow 517 is then input into the VGT flow equation module 505which may use an inverse system model to transform turbine flow 517 intoa VGT control command u_(vgt) 519. The VGT inversion model includesdetermining a desired flow through the turbine using manifoldflow/enthalpy balance as follows:

W _(t)=( P _(t) ,r _(HP) ,r _(Hp))+FBK(P _(i) −P _(i))  [52]

wherein FF is the feedfoward term,

-   -   FBK is the feedback term,    -   P ₁ is a target intake pressure, and    -   r _(HP) is a target high pressure EGR rate.        Target exhaust (turbine inlet) pressure is found from desired        boost and compressor flow using the turbocharger power balance.

$\begin{matrix}{{\frac{1}{\eta_{m}\eta_{t}\eta_{c}}*\frac{1}{T_{t,{in}}}*\frac{{\overset{\_}{W}}_{c}*T_{c,{in}}*\left\lbrack {\left( \frac{{\overset{\_}{P}}_{boost}}{P_{c,{in}}} \right) - 1} \right\rbrack}{\left( {{\overset{\_}{W}}_{c} + {\overset{\_}{W}}_{f}} \right)}} = {1 - \left( \frac{P_{t,{out}}}{{\overset{\_}{P}}_{t,{in}}} \right)^{\mu}}} & \lbrack 53\rbrack\end{matrix}$

Wherein a term x1 is equivalent to

${\frac{1}{T_{t,{in}}}*{\overset{\_}{W}}_{c}*T_{c,{in}}*\left\lbrack {\left( \frac{{\overset{\_}{P}}_{boost}}{P_{c,{in}}} \right) - 1} \right\rbrack},$

and a term x2 is equivalent to the sum of target compressor flow andtarget fuel flow. When terms x1 and x2 are input into a regression whichfits data based on x1 and x2 a value y is determined Target exhaustpressure may then be calculated based on the inversion (1−y)^(−1/μ). TheVGT position required for desired flow through turbine at the targetturbine inlet pressure may then be found using the following VGT flowrelationships.

$\begin{matrix}{W_{t} = {{A\left( u_{vgt} \right)}*\frac{{\overset{\_}{P}}_{t,{in}}}{\sqrt{{RT}_{t,{in}}}}{\Psi \left( \frac{{\overset{\_}{P}}_{t,{in}}}{P_{t,{out}}} \right)}}} & \lbrack 54\rbrack \\{{A\left( u_{vgt} \right)} = {\frac{W_{t}}{\Psi \left( \frac{{\overset{\_}{P}}_{t,{in}}}{P_{t,{out}}} \right)}*\frac{\sqrt{{RT}_{t,{in}}}}{P_{t,{out}}}*\frac{P_{t,{out}}}{{\overset{\_}{P}}_{t,{in}}}}} & \lbrack 55\rbrack\end{matrix}$

A term z1 is equivalent to

${\frac{W_{t}}{\Psi \left( \frac{{\overset{\_}{P}}_{t,{in}}}{P_{t,{out}}} \right)}*\frac{\sqrt{{RT}_{t,{in}}}}{P_{t,{out}}}},$

and a term z2 is equivalent to

$\frac{P_{t,{out}}}{{\overset{\_}{P}}_{t,{in}}}.$

When terms z1 and z2 are input into a regression which fits data basedon z1 and z2 a feedforward VGT position command u_(vgt) is determined.This command is then used to control the VGT of the air charging systemto achieve a target boost pressure.

FIG. 6 graphically depicts an exemplary EGR control scheme, including acomparison of a measured EGR rate and a desired EGR rate to an EGRactuator opening percentage, in accordance with the present disclosure.EGR rate is controlled using only the LP EGR loop. Plot 601 depicts EGRrate 604 as a function of time 603. Measured EGR rate is depicted asline 610. Desired rate is depicted as line 611. Plot 602 depicts EGRactuator opening percentage 605 as a function of time 603. As the EGRrate is being controlled using only the LP EGR loop, LP EGR actuatoropening position 612 is controlled to increase opening percentage 605stepwise as a function of time. HP EGR actuator opening position 613remains unopened at 0% throughout.

FIG. 7 graphically depicts an exemplary boost control scheme, whereinboth high-pressure EGR and low-pressure EGR flows are considered,including a comparison of a measured intake manifold pressure and adesired intake manifold pressure to a VGT actuator opening percentage,in accordance with the present disclosure. VGT feedforward control ismodel based, and incorporates how EGR is delivered, considering both LPEGR rate and HP EGR rates. Plot 701 depicts pressure 704 as a functionof time 703. Desired intake manifold pressure p_(i) is constant and isdepicted by line 711. Plot 702 depicts VGT actuator open percentage 705as a function of time 703. VGT actuator opening position 712 is shown.Measured intake manifold pressure 710 is shown achieving and trackingthe desired target boost (intake manifold pressure p_(i)) 711 as VGTactuator opening position 712 is modulated automatically using thefeedforward control methods in accordance with the present disclosure.

FIG. 8 graphically depicts exemplary data comparing actual VGT flow 811and estimated VGT flow 812, in accordance with the feedforward VGT modelof the present disclosure. Over sample size 802 the VGT flow fit 803between actual VGT flow 811 and estimated VGT flow 812 tracks closely.

FIG. 9 graphically depicts exemplary data comparing computed targetturbine inlet pressure 912 and measured target turbine inlet pressure911, in accordance with the feedforward VGT model of the presentdisclosure. Over sample size 902 the VGT flow fit 903 between actualcomputed target turbine inlet pressure 912 and measured target turbineinlet pressure 911 tracks closely.

FIG. 10 depicts an exemplary process of model-based feedforwardturbocharger control 1000 of an internal combustion engine including anEGR system with a high-pressure EGR loop and a low-pressure EGR loop, inaccordance with the present disclosure. Table 1 is provided as a keywherein the numerically labeled blocks and the corresponding functionsare set forth as follows.

TABLE 1 BLOCK BLOCK CONTENTS 1001 Monitor a target EGR rate and a targetintake manifold pressure 1002 Monitor an actual EGR rate 1003 Determinea compressor flow based on the target EGR rate, the target intakemanifold pressure and the actual EGR rate 1004 Monitor operatingconditions of a compressor in the air charging system and operatingconditions of a turbine in the air charging system 1005 Determine powerrequested by the compressor in the air charging system based on thecompressor flow, the target intake manifold pressure, and the monitoredoperating conditions of the compressor 1006 Determine power to begenerated by the turbine based upon the power requested by thecompressor 1007 Determine a turbine flow based upon the power to begenerated by the turbine, and the monitored operating conditions of theturbine 1008 Determine a system control command for the air chargingsystem based on the turbine flow and the monitored operating conditionsof the turbine 1009 Control the air charging system based on the systemcontrol command

The disclosure has described certain preferred embodiments andmodifications thereto. Further modifications and alterations may occurto others upon reading and understanding the specification. Therefore,it is intended that the disclosure not be limited to the particularembodiment(s) disclosed as the best mode contemplated for carrying outthis disclosure, but that the disclosure will include all embodimentsfalling within the scope of the appended claims.

1. Method of model-based control of an air charging system in aninternal combustion engine including an exhaust gas recirculation systemwith a high pressure exhaust gas recirculation loop and a low pressureexhaust gas recirculation loop, the method comprising: monitoring anactual exhaust gas recirculation rate; monitoring operating conditionsof a compressor in the air charging system and operating conditions of aturbine in the air charging system; determining a compressor flow basedon a target exhaust gas recirculation rate, a target intake manifoldpressure and the actual exhaust gas recirculation rate; determining apower requested by the compressor in the air charging system based onthe compressor flow, the target intake manifold pressure, and themonitored operating conditions of the compressor; determining a power tobe generated by the turbine based upon the power requested by thecompressor; determining a turbine flow based upon the power to begenerated by the turbine and the monitored operating conditions of theturbine; determining a system control command for the air chargingsystem based on the turbine flow and the monitored operating conditionsof the turbine; and controlling the air charging system based on thesystem control command.
 2. The method of claim 1, wherein the aircharging system comprises a variable geometry turbocharger, includingthe turbine and the compressor.
 3. The method of claim 1, whereinmonitoring the actual exhaust gas recirculation rate comprisesmonitoring an overall in-cylinder exhaust gas recirculation rateincorporating a rate of high pressure exhaust gas recirculation and therate of low pressure exhaust gas recirculation.
 4. The method of claim3, further comprising controlling the overall in-cylinder exhaust gasrecirculation rate using only low pressure exhaust gas recirculationsystem control valves.
 5. The method of claim 4, wherein the overallin-cylinder exhaust gas recirculation rate is expressed by the followingrelationship.r=r _(HP)+(1−r _(HP))*r _(LP) wherein r is the overall in-cylinderexhaust gas recirculation rate, r_(HP) is the high pressure exhaust gasrecirculation rate, r_(LP) is the low pressure exhaust gas recirculationrate.
 6. The method of claim 1, wherein the compressor flow isdetermined in accordance with the following relationship:$W_{c} = {\left( {1 - r_{HP}} \right)*\eta_{v}\frac{V_{d}}{120R*T_{i}}N*p_{i}}$wherein W_(c) is a compressor flow, r_(HP) is a high pressure exhaustgas recirculation rate, η_(v) is a volumetric efficiency, R is auniversal gas constant, T_(i) is a intake temperature, V_(d) is avolumetric displacement, N is a engine speed, and p_(i) is a intakemanifold pressure.
 7. The method of claim 1, wherein determining thesystem control command for the air charging system comprises:determining a target turbine inlet pressure based on a desired intakemanifold pressure and the compressor flow; and determining the systemcontrol command required to achieve the turbine flow at the targetturbine inlet pressure.
 8. The method of claim 1, wherein determiningthe power requested by the compressor in the air charging system basedon the compressor flow, the target intake manifold pressure, and themonitored operating conditions of the compressor comprises utilizing thefollowing relationship.$P_{c} = {W_{c}T_{uc}{{c_{p}\left\lbrack {\left( \frac{p_{i}}{p_{uc}} \right)^{\mu} - 1} \right\rbrack}/\eta_{c}}}$wherein P_(c) is a power requested by the compressor, W_(c) is acompressor flow, T_(uc) is a temperature upstream of the compressor,c_(p) is a specific heat under constant pressure, p_(i) is an intakepressure, p_(uc) is a pressure upstream of the compressor μ is aspecific heat ratio, and η_(c) is an efficiency of the compressor. 9.The method of claim 1, wherein determining a turbine flow based upon thepower to be generated by the turbine and the monitored operatingconditions of the turbine comprises utilizing the followingrelationship.$P_{t} = {c_{p}T_{x}W_{t}{\eta_{t}\left\lbrack {1 - \left\lbrack \frac{p_{s}}{p_{x}} \right\rbrack^{\mu}} \right\rbrack}}$wherein P_(t) is a power to be generated by the turbine, η_(t) is aturbine efficiency, T_(x) is an exhaust temperature, p_(s) is a turbineoutlet pressure, and p_(x) is an exhaust pressure.
 10. Method to controlan exhaust gas recirculation system having a high pressure exhaust gasrecirculation loop and a low pressure exhaust gas recirculation loop, anair throttle system, and an air charging system in an internalcombustion engine, the method comprising: monitoring desired operatingtarget commands for each of the high pressure exhaust gas recirculationloop, the low pressure exhaust gas recirculation loop, the air throttlesystem, and the air charging system; monitoring operating parameters ofthe air charging system; determining a feedback control signal for eachof the high pressure exhaust gas recirculation loop, the low pressureexhaust gas recirculation loop, the air throttle system and the aircharging system based upon the corresponding desired operating targetcommands and the operating parameters of the air charging system;determining a high pressure exhaust gas recirculation flow in the highpressure exhaust gas recirculation loop, low pressure exhaust gasrecirculation flow in the low pressure exhaust gas recirculation loop,an air flow in the air throttle system and a turbine power transferratio in the air charging system based upon the corresponding feedbackcontrol signals for each of the high pressure exhaust gas recirculationloop, the low pressure exhaust gas recirculation loop the air throttlesystem and the air charging system; determining a system control commandfor each of the high pressure exhaust gas recirculation loop, the lowpressure exhaust gas recirculation loop, the air throttle system, andthe air charging system based on said high pressure exhaust gasrecirculation flow, said low pressure exhaust gas recirculation flow,said air flow and said turbine power transfer ratio; and controlling theair charging system based on said system control commands.
 11. Themethod of claim 10, wherein the desired operating target commandscomprise: a desired intake manifold pressure command, a desiredcompressor pressure ratio command, a desired burned gas fraction beforethe compressor command, and a desired burned gas fraction at the intakecommand.
 12. The method of claim 10, further comprising determining afeed forward control command for each of the high pressure exhaust gasrecirculation loop, the low pressure exhaust gas recirculation loop, theair throttle system and the air charging system based on thecorresponding desired operating target commands.
 13. The method of claim12, wherein determining said high pressure exhaust gas recirculationflow, said low pressure exhaust gas recirculation flow, said air flowand said turbine power transfer ratio is further based on thecorresponding feed forward control commands.
 14. The method of claim 12,wherein determining the feed forward control command for the aircharging system comprises: monitoring a target exhaust gas recirculationrate and a target intake manifold pressure; monitoring an actual exhaustgas recirculation rate; determining a compressor flow from a compressorin the air charging system based on the target exhaust gas recirculationrate, the target intake manifold pressure and the actual exhaust gasrecirculation rate; monitoring operating conditions of the compressorand operating conditions of a turbine in the air charging system;determining power requested by the compressor based on the compressorflow, the target intake manifold pressure, and the monitored operatingconditions of the compressor; determining power to be generated by theturbine based upon the power requested by the compressor; determining aturbine flow based upon the power to be generated by the turbine, andthe monitored operating conditions of the turbine; and determining afeed forward control command for the air charging system based on theturbine flow and the monitored operating conditions of the turbine. 15.The method of claim 10, wherein determining a system control command foreach of the high pressure exhaust gas recirculation loop, the lowpressure exhaust gas recirculation loop, the air throttle system, andthe air charging system comprises utilizing an inverse model of each ofthe high pressure exhaust gas recirculation loop, the low pressureexhaust gas recirculation loop, the air throttle system, and the aircharging system.
 16. The method of claim 10, wherein the air chargingsystem comprises a variable geometry turbocharger, including a turbineand a compressor.
 17. The method of claim 14, wherein monitoring anactual exhaust gas recirculation rate comprises monitoring an overallin-cylinder exhaust gas recirculation rate incorporating a rate of highpressure exhaust gas recirculation and a rate of low pressure exhaustgas recirculation.
 18. The method of claim 10, further comprisingcontrolling an overall in-cylinder exhaust gas recirculation rate, madeup of a combination of a high pressure exhaust gas recirculation rateand a low pressure exhaust gas recirculation rate, using only lowpressure exhaust gas recirculation system control valves.
 19. Method ofmodel-based feedforward control of an air charging system in an internalcombustion engine including an exhaust gas recirculation system with ahigh pressure exhaust gas recirculation loop and a low pressure exhaustgas recirculation loop, the method comprising: providing a physics basedair and charging system model of the internal combustion engine;applying model-based nonlinear control to the physics based air andcharging system model of the internal combustion engine, comprisingapplying physics model-based multivariable feedforward control to thephysics based air and charging system model; applying feedback controlto the physics based air and charging system model; transforming desiredair and charging targets for the air and charging system model toindividual flow or power signals for each of an exhaust gasrecirculation actuator, an air intake throttle valve actuator and avariable geometry turbocharger actuator; determining an actuatorposition for each of the exhaust gas recirculation actuator, air intakethrottle valve actuator and variable geometry turbocharger actuatorbased on the respective individual flow or power signals.
 20. The methodof claim 19, wherein the physics based air and charging system model isexpressed by the following system relationships:${\overset{.}{p}}_{rc} = {{{- {{cP}_{c}\left( {p_{rc},\frac{W_{c}\sqrt{T_{uc}}}{p_{uc}}} \right)}} + {J\left( {{\overset{.}{W}}_{c}W_{c}} \right)} + {{cP}_{t}\begin{bmatrix}{\frac{V_{i}}{{RT}_{i}}{\overset{.}{P}}_{i}} \\{m_{i}{\overset{.}{F}}_{i}} \\{m_{c}{\overset{.}{F}}_{c}}\end{bmatrix}}} = {\begin{bmatrix}{- W_{cyl}} \\0 \\0\end{bmatrix} + {\begin{bmatrix}1 & 1 & 0 \\{F_{c} - F_{i}} & {F_{x} - F_{i}} & 0 \\{- F_{c}} & 0 & {F_{x}\left( {t - \tau} \right.}\end{bmatrix}\begin{bmatrix}W_{itv} \\W_{{egr},{HP}} \\W_{{egr},{LP}}\end{bmatrix}}}}$ wherein V_(i) is an intake volume, R is a universalgas constant, T_(i) is an intake temperature, T_(uc) is a temperatureupstream of the compressor, P_(uc) is a pressure upstream of thecompressor, P_(i) is an intake pressure, m_(i) is an intake mass, m_(c)is an air mass before the compressor (at the low pressure EGR fixpoint), F_(i) is a burned gas fraction at the intake, F_(c) is theburned gas fraction before the compressor (at the low pressure EGR fixpoint), F_(x) is a burned gas fraction at the exhaust, W_(cyl) is a flowthrough the cylinder, W_(egr,HP) is a flow through the high pressureexhaust gas recirculation valve, W_(egr,LP) is a flow through the lowpressure exhaust gas recirculation valve, t is time, and τ is a timedelay.